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  Unbalanced Wheels 

One of the oldest forms of perpetual motion machine is the unbalanced wheel. This starts with the idea that everybody knows, which is that if you drop a weight it will fall and you need to keep your feet out of the way.
Rotating Weights
 Also everybody can understand that if you attach the weight to the outside of a wheel then you let it go, the wheel will rotate. But how far will it go? The answer is if the wheel is mounted on a frictionless bearing then it will rotate until the weight is at the same height as it was when you let it go. It will not complete a full circle.
 
This is because when it starts out it has a potential energy because of the gravitational attraction between the earth and the mass of the weight (the same rules apply if you use a magnet instead of gravity). As it falls it speeds up until it reaches the bottom of the wheel when all the potential energy has been converted to the energy of motion or kinetic energy.
 
Because the weight can’t fall any further it has no more potential energy and now the weight starts to rise on the other side of the wheel’s path and slow down as it rises. Eventually it will rise back to the height at which it started. Just like a child’s swing in a playground. At that point it has no more kinetic energy because it has stopped moving. All the energy has been converted back to potential energy. Or at least it would if the wheel was mounted on a frictionless bearing. To find out more about energy and power click here.
 
If there is any friction in the bearing then the weight won’t quite get back to the height it was before. This is because some of the potential energy will have been used on overcoming the friction in the bearing. So it will rock backwards and forwards, each time a little lower than the last until eventually it stops. Just like the child on the swing if you don’t keep pushing them.

The next step was to think of a way of keeping the wheel unbalanced all the time so that just before the first weight stopped moving a new one took its place. The result was a series of ancient machines like this one. The theory is that as the wheel turns the weights fall out further from the centre of the wheel and therefore have more leverage (torque) on one side of the wheel than the weights on the other side. At first sight it looks inevitable that the wheel will rotate.
In fact it will, but just like the example above it won’t complete a full rotation and for the same reasons. But it gets more complicated because many machines of this type need some external source of energy such as a human being to put them in a position where they will move at all, and that initial ‘kick’ can often cause them to move for quite a long time and even rotate fully. This problem applies to many types of perpetual motion machine that almost invariably are not ‘self starting’ where it is in fact only the initial energy input that creates the illusion of free motion. We do not have to look further back than our first example. If no one lifts the weight up to its initial height then it can never fall on your feet. So it is with these wheels. Someone has to lift one of the weights to start the thing moving.
 
So perhaps it does look as though it should keep moving, but if you look carefully you will see that there are more weights on the left than there are on the right, but they are nearer the middle. The result is that the average distance of the weights to the centre on the left is smaller than the average distance of the weights to the centre on the right. But there are more weights on the left.
It turns out that the leverage on the left, which is the total weight times the average distance (the average torque) is exactly the same as the larger distance on the right times the total smaller weight on the right. If it starts out unbalanced the wheel will rock backwards and forwards until this balance occurs, when it won’t move any more. The only reason that it moves at all is because someone has unbalanced it first by moving one of the weights.
 
The first example of such a machine was recorded nearly 1000 years ago by an Indian philosopher called Bhaskara who devised a wheel that used mercury instead of falling weights. The machine shown here is by Villard de Honnecourt from about 100 years later.
 
 
 
This has been a long explanation of these simple machines because they illustrate some major principles. Firstly in order to keep moving an external source of energy is required. This is the first law of thermodynamics. Secondly, that part of the energy supplied will be used up in overcoming the internal friction (and air friction) of the machines. This is the second law of thermodynamics.
Variations on this type of machine often use fixed magnets or buoyancy instead of the force of gravity, but the result (and most of the arithmetic)  is always the same. If the machines move at all it is because of the intial work done to unbalance the forces acting on the machine and they all soon come to a halt because of internal friction.
 
 
The unbalanced wheel violates the first law of thermodynamics because it has no external source of energy and therefore cannot do useful work. The second law of thermodynamics says that any initial surplus energy given to it by a ‘starting push’ will soon be used up by internal friction.